Experimental demonstration of a transparent graphene millimetre wave absorber with 28% fractional bandwidth at 140 GHz

Bian Wu1,3, Hatice M. Tuncer2, Majid Naeem1, Bin Yang1,4, Matthew T. Cole2,

William I. Milne2, Yang Hao1,*

1 School of Electronic Engineering and Computer Science, Queen Mary University of London, London, E1 4NS, United Kingdom;

2 Department of Engineering, University of Cambridge, 9 JJ Thomson Avenue, Cambridge, CB3 0FA, United Kingdom;

3 School of Electronic Engineering, Xidian University, Xi’an, 710071, China;

4 Engineering, Sports & Sciences Academic Group, University of Bolton, Deane Road, Bolton, BL3 5AB, United Kingdom.

* Email:

The development of transparent radio-frequency electronics has been limited, until recently, by the lack of suitable materials. Naturally thin and transparent graphene may lead to disruptive innovations in such applications. Here, we realize optically transparent broadband absorbers operating in the millimetre wave regime achieved by stacking graphene bearing quartz substrates on a ground plate. Broadband absorption is a result of mutually coupled Fabry-Perot resonators represented by each graphene-quartz substrate. An analytical model has been developed to predict the absorption performance and the angular dependence of the absorber. Using a repeated transfer-and-etch process, multilayer graphene was processed to control its surface resistivity. Millimetre wave reflectometer measurements of the stacked graphene-quartz absorbers demonstrated excellent broadband absorption of 90% with a 28% fractional bandwidth from 125-165 GHz. Our data suggests that the absorbers’ operation can also be extended to microwave and low-terahertz bands with negligible loss in performance.

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Graphene has attracted much attention in recent years due to its extraordinary electronic and optical properties such as high electron mobility, truly atomic thickness, mechanical flexibility and saturable absorption [1–5]. With an optical transparency of 97-98% [6] and an undoped sheet resistance of the order of 6000 Ω/sq [7] to ~125 Ω/sq [8], monolayer graphene films have found, not unsurpisingly, many applications where low sheet resistance and high optical transparency are essential. Chemical vapour deposition (CVD) permits the synthesis of high quality, large-area graphene films [9-13] and an increased number of layers provides lower sheet resistances necessary for transparent conducting applications. Few layer graphene films with sheet resistance of 280 Ω/sq (80% transparent) and 770 Ω/sq (90% transparent), synthesized on Ni films [11-12], and 350 Ω/sq (90% transparent) on Cu films [13], make CVD graphene one of the few viable substitute materials for the mechanically inflexible transparent conducting oxides; indium tin oxide (ITO) or fluorine-doped tin oxide (FTO) [14-15], in almost all transparent electronic devices [16-17]. Chemical doping has been shown to further reduce the sheet resistance of graphene films [18]. Until present most advances in graphene devices have focussed on the terahertz and optical frequencies, while in the radio-frequency regime, where the sheet resistivity dominates, the practical applications of graphene has been towards graphene-based FET mixers [19-21], RF transistors [22-24] and controllable resistive devices such as metasurfaces [25-29] or absorbers [30, 31]. However, the experimental demonstration of transparent radio-frequency absorbers, with broadband properties, still requires further research.

Radar absorbing materials (RAMs) significantly reduce an object'sobservable radar cross-sectionwithin specific bandwidths [32]. A Salisbury screen absorber consists of a thin resistive sheet and a ground separated by a quarter wavelength dielectric filler [33, 34]. It operates by matching the absorber characteristic impedance to free space and the effective open circuit created leads to reduced reflections at the surface. However, the operation is narrowband and suffers from reduced absorption capability if the angle of incidence is not perpendicular to the absorber [32]. Nevertheless, if the number of screens can be increased, using multiple layers of thin resistive sheets with the filling dielectric, one can form a Jaumann absorber, which offers an extended bandwidth and reduced angular sensitivity [32,35]. Though very functional, the added layers and consequent increased thickness, make Jaumann screens a bulky alternative. Thus, there is a clear need to reduce the thickness of the broadband absorber components [33], with materials which have a characteristic impedance of the same order of magnitude as the free space impedance; graphene is one such leading candidate.

In this letter, we report for the first time on the fabrication and characterization of transparent broadband absorbers consisting of several stacked multilayer graphene sheets on quartz substrates backed with a ground plate. The large-area CVD multilayer graphene films have been fabricated through a repeated etch-and-transfer process to minimise PMMA residue between the layers, thereby yielding high-quality and optically transparent multilayer graphene films. Herein, analytical expressions are developed for the reflection and absorption coefficients consisting of an arbitrary number of stacked graphene layers. These expressions serve as a practical design guide to estimate the influence of the sheet resistance and substrate parameters, as well as the impact of oblique incidence. To validate the broadband absorption, millimetre wave reflectometer experiments have been carried out with single and stacked absorbers from 110 GHz to 170 GHz. For 5-unit stacked structures, 90% absorbance can be achieved with 28% fractional bandwidth from 125 GHz to 165 GHz. The broadband absorption can be further improved by using thinner substrates with lower relative permittivity or stacking more graphene-quartz substrates at the expense of reduced optical transparency.

a / b /
c / / d /

Figure 1 | Schematic and optical images of multilayer graphene on quartz and stacked graphene-quartz absorbers. (a) Schematic of the multiple transfer-etch processing for a 2L device; (b) Typical UV-Vis spectra for the 1.3 mm thick bare quartz and 1-4L graphene samples; (c) Schematic of the N-unit stacked absorber and the equivalent transmission-line circuit model; (d) Optical images of 2L and 3L graphene samples and N = 1-4 stacked graphene-quartz structures backed with a ground plate (N is the number of stacked graphene-quartz units).

Results

Fabrication and modelling of the stacked graphene-quartz absorber. CVD graphene films were grown on four inch Cu/SiO2/Si wafers and were found, by optical and electron microscopy to be free of pin-holes. Samples were of high uniformity with > 90% monolayer coverage, as confirmed by Raman spectroscopic mapping and optical microscopy [36]. Films were transferred to fused silica quartz substrates using spin-coated 200 nm thick poly (methyl methacrylate) (PMMA) as the supporting layer (for details see Methods section) (Fig. 1a). Multilayer graphene samples were processed by a multiple transfer-and-etch method. This involves repetitive transfer of the PMMA-graphene films onto diced graphene on Cu/SiO2/Si substrates and etching them in an aqueous ammonium persulfate solution before finally transferring the released PMMA/graphene onto the quartz substrates. This method avoids significant PMMA residue build-up between the stacks of graphene layers yielding reduced mean sheet resistance of ~0.9 kΩ/sq for 2L and ~0.6 kΩ/sq for 3L. The number of graphene layers was confirmed via UV-Vis spectro-photometery. Optical transmittances of 85%-91% at 700 nm for 1-4L graphene was noted (Fig. 1b).

The proposed broadband absorber was realized by stacking multilayer graphene bearing quartz samples on top of a ground plate, as depicted in Fig. 1c. Fig. 1d illustrates optical images of quartz-supported 2L and 3L graphene layers (17 mm 8.5 mm). The N-unit samples, with similar sheet resistances, were stacked onto a ground plate to construct the broadband absorbers, as shown in Fig. 1d.

To predict the absorber performance, we have derived an analytical expression based on a circuit model equivalent, as shown in Fig. 1c. For simplicity, it is assumed that all of the graphene sheets have the same surface conductivity and the quartz substrates are homogeneous and isotropic with a permittivity of and a thickness of. The absorber model is assumed infinite in the xy plane and stacked along the z direction. A uniform transverse electromagnetic (TEM) plane wave is assumed to arrive at the absorber surface with an oblique incidence angle of. Since the thickness of quartz is a few millimetres, high-order modes become evanescent and can be ignored in the millimetre wave regime. The graphene sheets can be modelled as thin, two-sided surfaces characterized by surface conductivity, which is governed by the intraband contributions at low-terahertz frequencies and can be expressed as [37]

(1)

where is the radian frequency, is the chemical potential, is the phenomenological scattering rate, is temperature, is the charge of an electron, is the reduced Planck’s constant andis the Boltzmann’s constant. Although is frequency dependent in equation (1), in the millimetre wave region the conductance term remains almost constant, whilst the susceptance term tends to 0 and can thus be neglected; is dominated by the surface conductance and can be regarded as frequency independent.

In terms of TEM transmission line theory, the quartz substrate can be modelled as a dielectric with propagation constant and characteristic admittance, with the resistive graphene sheets represented as a shunt admittance,, where is the sheet resistance (Fig. 1c). The propagation constant of free space is denoted by and the characteristic admittance by. The general analytical expressions for TE and TM polarizations of a wave with incident angle can be expressed as [38]

,, (2)

, (3)

, (4)

whereis the speed of light in vacuum, is the angular frequency, and is the intrinsic free space wave impedance.

For a single (N = 1) graphene-quartz absorber, the input admittance is given by

(5)

While for the N-unit stacked graphene-quartz absorber, the input admittance can be derived as

( i = 1, 2 …, N) (6)

Since there is no transmission due to total reflection on the ground surface, we obtain the reflection coefficient and absorption coefficient of the stacked graphene-quartz absorber from

Figure 2 | Millimetre wave reflectometer measurements. (a) Photograph of the experimental set-up. Red lines refer to the incident wave from the transmitter to the sample; green lines represent the reflected wave from the sample to the receiver. The H-grating transmits vertically polarized waves but reflects horizontally polarized waves. The 45D grating selects the E-field components with 45˚ rotation. (b) Photograph of the transparent absorber consisting of graphene-quartz samples backed with a metal plate.

(7)

(8)

The highest absorption is achieved when or; the absorption peaks correspond to reflection zeros. In this case the incident wave will go through multiple reflections and be fully absorbed by the lossy resistive graphene sheets.

Measurement and prediction of transparent graphene-quartz absorbers. In order to investigate the nanostructured absorber, reflection spectra are measured by a well-established free space millimetre wave reflectometery technique and then transformed to absorption spectra according to equation (8). The experimental set-up is illustrated in Fig. 2a. The reflectometer functions at frequencies from 110 GHz up to 170 GHz using a HP N5244A vector network analyzer fitted with millimetre wave extension heads (see Methods section).

Firstly, single (N = 1) absorbers with 1-4L graphene were measured and then two graphene-quartz samples were stacked together to construct a 2-unit (N = 2) absorber (Fig. 2b). Measurements up to N = 5 were performed. The stacked graphene-quartz structures were backed with a conducting ground plate which was fixed to the metal support, guaranteeing that the sample was perpendicular to the incident wave. Only the normal incidence is considered here. Each graphene adlayer was 17 mm8.5 mm and covered the beam width of the incidence wave.

a / b
c / d

Figure 3 | Comparison of calculated and measured spectra of single graphene-quartz absorbers. (a, c) Calculated absorption spectra. The scattering rates are chosen as = 7 meV for= 0.0 eV and = 5 meV for all others, = 300 K. (b, d) Measured reflection and absorption spectra of single (N = 1) graphene-quartz absorbers with 1-4L graphene on quartz ( and = 1.3 mm). The measurements show that the improvement in absorption is substantial from 1L to 2L multilayer graphene while less significant after 2L. The improved absorption is attributed to the reduced sheet resistance which is analogous to increasing the chemical potential of monolayer graphene in the calculation.

The measured reflection and absorption spectra of single graphene-quartz absorbers with 1-4L graphene on quartz are compared with analytical calculations in Fig. 3. The effect of increasing the number of graphene layers, which reduces the sheet resistance, is analogous to increasing the chemical potential. The calculated results in Fig. 3a and 3c show the influence of the chemical potential on

the reflection and absorption properties of the absorber. When= 0 eV and = 7 meV, this corresponds to a sheet resistance of 5044 Ω/sq which makes the input impedance challenging to match with free space. The peak absorption is lower than 40% indicating a poor

absorption. As the chemical potential increases, in steps of = 0.1 eV, the sheet resistance of graphene is reduced and the peak absorption improves. When= 0.3 eV and = 5 meV, the corresponding sheet resistance is 430 Ω/sq, which tends toward the free space impedance. Good impedance matching leads to 100% peak absorption around 148 GHz.

Presently available monolayer CVD graphene often has a sheet resistance of > 1000 Ω/sq. In order to reduce the sheet resistance, one method is to increase its chemical potential. This usually requires electrostatic biasing or chemical doping [37,18,39]. Alternatively, we can increase the number of graphene layers to reduce the total sheet resistance [39]. This effect has been validated in the single absorber measurements in Fig. 3b and 3d.

First, the bare quartz substrate on the ground plate was tested in the reflectometer as a background reference. A total reflection with no absorption is observed across the whole frequency range, except for the intrinsic systematic noise at high frequencies (> 160 GHz). The single unit graphene-quartz absorbers with 1-4L graphene were then measured. A 1L absorber has a small absorption peak around 30% at 148 GHz, which is similar to the case of = 0.0 eV and = 7 meV (Fig. 3c, d). In contrast, a 2L absorber has a peak absorption around 95%, which is similar to the calculated case of= 0.2 eV and = 5 meV. A small frequency shift is caused by the thickness variation in the practical quartz slabs (±2%) and the air gap (~0.1 mm) between quartz and ground plate. The absorption peak increase marginally (+1.2%) for the 3L case and fall slightly (-1%) for the 4L case. Multilayer graphene can thusly be used to derive a turbostratic, stacked, artificial graphite-like material of sufficiently reduced sheet resistance capable of near matching the free space impedance; however, it is challenging to improve the sheet resistance further for samples consisting of more than 3 layers, which could be due to water residue between the layers that prevents good contact between the interfacing layers in the present samples.